Moving Coil Galvanometer

• Device used to detect and measure electric currents
• Consists of a coil of wire and a permanent magnet
• When current passes through the coil, it experiences a torque
• The coil rotates, indicating the presence and magnitude of the current

Moving Coil Galvanometer as an Ammeter

• An ammeter is used to measure the current flowing through a circuit
• A galvanometer can be converted into an ammeter by connecting a shunt resistor in parallel
• The shunt resistor diverts most of the current, allowing only a fraction to pass through the galvanometer
• The galvanometer is calibrated to display the correct current based on the fraction passing through

Moving Coil Galvanometer as a Voltmeter

• A voltmeter is used to measure the potential difference (voltage) across a circuit component
• A galvanometer can be converted into a voltmeter by connecting a series resistor
• The series resistor limits the current passing through the galvanometer to a safe value
• The galvanometer is calibrated to display the correct voltage based on the current passing through

Potential Energy of a Dipole

• A dipole is a pair of equal and opposite charges separated by a distance
• The potential energy of a dipole in a uniform electric field can be calculated using the formula:
  • $U = -p \cdot E \cdot \cos(\theta)$ where $U$ is the potential energy, $p$ is the dipole moment, $E$ is the electric field strength, and $\theta$ is the angle between the dipole moment and electric field

Electric Potential Energy of a System of Charges

• The electric potential energy of a system of charges is the sum of the potential energy between each pair of charges in the system
• For two charges, the potential energy can be calculated using the formula:
  • $U = \frac{k \cdot q_1 \cdot q_2}{r}$ where $U$ is the potential energy, $k$ is the Coulomb constant, $q_1$ and $q_2$ are the charges, and $r$ is the distance between the charges

Electric Potential Difference

• Electric potential difference, also known as voltage, is the work done per unit charge in moving a charge between two points in an electric field
• It is denoted by the symbol $\Delta V$ and is given by the formula:
  • $\Delta V = \frac{W}{q}$ where $\Delta V$ is the potential difference, $W$ is the work done, and $q$ is the charge

Kirchhoff’s Laws

• Kirchhoff’s laws are two fundamental principles used to analyze electrical circuits
• Kirchhoff’s first law, also known as the law of conservation of charge, states that the sum of currents entering a junction is equal to the sum of currents leaving it
• Kirchhoff’s second law, also known as the voltage law, states that the algebraic sum of all the potential differences in any closed loop in a circuit is equal to zero

Resistors in Series

• Resistors connected in series have the same current passing through them
• The total resistance of resistors in series is equal to the sum of their individual resistances
• The potential difference across each resistor is proportional to its resistance: $V_1 : V_2 : V_3 = R_1 : R_2 : R_3$

Resistors in Parallel

• Resistors connected in parallel have the same potential difference across them
• The total resistance of resistors in parallel can be calculated using the formula:
  • $\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$
• The total current passing through the resistors is equal to the sum of the individual currents: $I_{\text{total}} = I_1 + I_2 + I_3$

Capacitors in Series

• Capacitors connected in series have the same charge stored on them
• The reciprocal of the total capacitance of capacitors in series can be calculated using the formula:
  • $\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}$
• The potential difference across each capacitor is inversely proportional to its capacitance: $\frac{V_1}{V_2} = \frac{C_2}{C_1}$

Magnetic Field Due to Current

• A current-carrying wire produces a magnetic field around it
• The direction of the magnetic field can be determined using the right-hand rule
• The magnitude of the magnetic field at a distance $r$ from a straight wire carrying current $I$ is given by:
  • $B = \frac{\mu_0 \cdot I}{2\pi \cdot r}$ where $B$ is the magnetic field, $\mu_0$ is the permeability of free space, and $r$ is the distance from the wire

Magnetic Field Inside a Solenoid

• A solenoid is a coil of wire with many loops
• Inside a solenoid, the magnetic field is nearly uniform and parallel to the axis
• The magnitude of the magnetic field inside a solenoid is given by:
  • $B = \mu_0 \cdot n \cdot I$ where $B$ is the magnetic field, $\mu_0$ is the permeability of free space, $n$ is the number of turns per unit length, and $I$ is the current

Magnetic Force on a Moving Charge

• A moving charge experiences a magnetic force when it enters a magnetic field
• The magnetic force on a moving charge can be calculated using the formula:
  • $\vec{F} = q \cdot \vec{v} \times \vec{B}$ where $\vec{F}$ is the magnetic force, $q$ is the charge, $\vec{v}$ is the velocity, and $\vec{B}$ is the magnetic field

Torque on a Current-Carrying Loop

• A current-carrying loop placed in a magnetic field experiences a torque
• The torque on a current-carrying loop can be calculated using the formula:
  • $\vec{\tau} = \vec{N} \times \vec{B}$ where $\vec{\tau}$ is the torque, $\vec{N}$ is the magnetic moment, and $\vec{B}$ is the magnetic field

Faraday’s Law of Electromagnetic Induction

• Faraday’s law states that a change in magnetic field induces an electromotive force (emf) in a loop of wire
• The induced emf can be calculated using the formula:
  • $|\varepsilon| = N \cdot \frac{d\Phi_B}{dt}$ where $|\varepsilon|$ is the magnitude of the induced emf, $N$ is the number of turns in the loop, and $\frac{d\Phi_B}{dt}$ is the rate of change of magnetic flux

Lenz’s Law

• Lenz’s law states that the direction of the induced current is such that it opposes the change that produced it
• This law is based on the principle of conservation of energy
• Lenz’s law can be used to determine the direction of induced currents in various situations

Self-Inductance

• Self-inductance is a property of a circuit that opposes changes in current
• The self-inductance of a coil can be calculated using the formula:
  • $L = \frac{N\Phi_B}{I}$ where $L$ is the self-inductance, $N$ is the number of turns, $\Phi_B$ is the magnetic flux, and $I$ is the current

Mutual Inductance

• Mutual inductance is a property of two or more circuits that affect each other’s magnetic fields
• The mutual inductance between two coils can be calculated using the formula:
  • $M = \frac{N_2\Phi_{B1}}{I_1} = \frac{N_1\Phi_{B2}}{I_2}$ where $M$ is the mutual inductance, $N_1$ and $N_2$ are the number of turns, $\Phi_{B1}$ and $\Phi_{B2}$ are the magnetic fluxes, and $I_1$ and $I_2$ are the currents

Alternating Current (AC)

• Alternating current is a type of current that periodically changes direction
• AC is commonly used for power transmission and distribution
• The value of AC is typically described by its amplitude, frequency, and phase

Power in AC Circuits

• The power in an AC circuit can be calculated using the formula:
  • $P = V \cdot I \cdot \cos(\theta)$ where $P$ is the power, $V$ is the voltage, $I$ is the current, and $\theta$ is the phase angle

Moving Coil Galvanometer

• Device used to detect and measure electric currents
• Consists of a coil of wire and a permanent magnet
• When current passes through the coil, it experiences a torque
• The coil rotates, indicating the presence and magnitude of the current
• It can be used as an ammeter or a voltmeter

Moving Coil Galvanometer as an Ammeter

• An ammeter is used to measure the current flowing through a circuit
• A galvanometer can be converted into an ammeter by connecting a shunt resistor in parallel
• The shunt resistor diverts most of the current, allowing only a fraction to pass through the galvanometer
• The galvanometer is calibrated to display the correct current based on the fraction passing through
• Example: A galvanometer with a shunt resistor of 0.1 ohms can measure currents up to 10A

Moving Coil Galvanometer as a Voltmeter

• A voltmeter is used to measure the potential difference (voltage) across a circuit component
• A galvanometer can be converted into a voltmeter by connecting a series resistor
• The series resistor limits the current passing through the galvanometer to a safe value
• The galvanometer is calibrated to display the correct voltage based on the current passing through
• Example: A galvanometer with a series resistor of 1000 ohms can measure voltages up to 100V

Potential Energy of a Dipole

• A dipole is a pair of equal and opposite charges separated by a distance
• The potential energy of a dipole in a uniform electric field can be calculated using the formula:
  • $U = -p \cdot E \cdot \cos(\theta)$ where $U$ is the potential energy, $p$ is the dipole moment, $E$ is the electric field strength, and $\theta$ is the angle between the dipole moment and electric field
• Example: A dipole with a dipole moment of 2 Cm and an electric field of 100 N/C at an angle of 30 degrees has a potential energy of -100 J

Electric Potential Energy of a System of Charges

• The electric potential energy of a system of charges is the sum of the potential energy between each pair of charges in the system
• For two charges, the potential energy can be calculated using the formula:
  • $U = \frac{k \cdot q_1 \cdot q_2}{r}$ where $U$ is the potential energy, $k$ is the Coulomb constant, $q_1$ and $q_2$ are the charges, and $r$ is the distance between the charges
• Example: Two charges of +2 C and -3 C separated by a distance of 5 m have a potential energy of -24 J

Electric Potential Difference

• Electric potential difference, also known as voltage, is the work done per unit charge in moving a charge between two points in an electric field
• It is denoted by the symbol $\Delta V$ and is given by the formula:
  • $\Delta V = \frac{W}{q}$ where $\Delta V$ is the potential difference, $W$ is the work done, and $q$ is the charge
• Example: If 10 J of work is done to move a charge of 2 C between two points, the potential difference between them is 5 V

Kirchhoff’s Laws

• Kirchhoff’s laws are two fundamental principles used to analyze electrical circuits
• Kirchhoff’s first law, also known as the law of conservation of charge, states that the sum of currents entering a junction is equal to the sum of currents leaving it
• Kirchhoff’s second law, also known as the voltage law, states that the algebraic sum of all the potential differences in any closed loop in a circuit is equal to zero
• Example: In a circuit, if three currents enter a junction with values 2A, 3A, and 4A, the sum of the currents leaving the junction must be 9A

Resistors in Series

• Resistors connected in series have the same current passing through them
• The total resistance of resistors in series is equal to the sum of their individual resistances
• The potential difference across each resistor is proportional to its resistance: $V_1 : V_2 : V_3 = R_1 : R_2 : R_3$
• Example: Three resistors with values 2 ohms, 3 ohms, and 4 ohms connected in series have a total resistance of 9 ohms

Resistors in Parallel

• Resistors connected in parallel have the same potential difference across them
• The total resistance of resistors in parallel can be calculated using the formula:
  • $\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$
• The total current passing through the resistors is equal to the sum of the individual currents: $I_{\text{total}} = I_1 + I_2 + I_3$
• Example: Three resistors with values 2 ohms, 3 ohms, and 4 ohms connected in parallel have a total resistance of 1.2 ohms

Capacitors in Series

• Capacitors connected in series have the same charge stored on them
• The reciprocal of the total capacitance of capacitors in series can be calculated using the formula:
  • $\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}$
• The potential difference across each capacitor is inversely proportional to its capacitance: $\frac{V_1}{V_2} = \frac{C_2}{C_1}$
• Example: Three capacitors with values 2 F, 3 F, and 4 F connected in series have a total capacitance of 0.545 F